Higher categories, colimits, and the blob complex

We summarize our axioms for higher categories, and describe the blob complex. Fixing an n-category C, the blob complex associates a chain complex B_*(W;C)$ to any n-manifold W. The 0-th homology of this chain complex recovers the usual topological quantum field theory invariants of W. The higher homology groups should be viewed as generalizations of Hochschild homology (indeed, when W=S^1 they coincide). The blob complex has a very natural definition in terms of homotopy colimits along decompositions of the manifold W. We outline the important properties of the blob complex, and sketch the proof of a generalization of Deligne's conjecture on Hochschild cohomology and the little discs operad to higher dimensions.Comment: 7 page

The centre of the extended Haagerup subfactor has 22 simple objects

We explain a technique for discovering the number of simple objects in $Z(C)$, the center of a fusion category $C$, as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring $K(C)$ and the dimension function $K(C) \to \mathbb{C}$. The method is not guaranteed to succeed (it may give spurious answers besides the correct one, or it may simply take too much computer time), but it seems it often does. We illustrate by showing that there are 22 simple objects in the center of the extended Haagerup subfactor [arXiv:0909.4099].Comment: 10 page

Heroic failures in disseminating novel e learning technologies to corporate clients: a case study of interactive webcasting

In principle, it should be easier to disseminate novel learning concepts based in technology enhanced learning to companies. Unfortunately, many corporations seem to be extremely risk averse, and the challenges inherent in the new models seem to be very hard for them to accept. This paper uses the deployment of interactive webcasting systems to present a series of case studies of dissemination successes and failures. We will suggest that the key to successful deployment is in making critical innovation (and its risk) invisible to the client, whilst matching their expectations with an "appropriate" level of technology. This work has led to a new dissemination portal "Prolearn.TV"

Dissing States?: Invalidation of State Action During the Rehnquist Era

Used by permission of the Virginia Law Review Association

Resonant Relaxation in Stellar Systems

We demonstrate the existence of an enhanced rate of angular momentum relaxation in nearly Keplerian star clusters, such as those found in the centers of galactic nuclei containing massive black holes. The enhanced relaxation arises because the radial and azimuthal orbital frequencies in a Keplerian potential are equal, and hence may be termed {\em resonant relaxation}. We explore the dynamics of resonant relaxation using both numerical simulations and order-of-magnitude analytic calculations. We find that the resonant angular momentum relaxation time is shorter than the non-resonant relaxation time by of order $M_\star/M$, where $M_\star$ is the mass in stars and $M$ is the mass of the central object. Resonance does not enhance the energy relaxation rate. We examine the effect of resonant relaxation on the rate of tidal disruption of stars by the central mass; we find that the flux of stars into the loss cone is enhanced when the loss cone is empty, but that the disruption rate averaged over the entire cluster is not strongly affected. We show that relativistic precession can disable resonant relaxation near the main-sequence loss cone for black hole masses comparable to those in galactic nuclei. Resonant dynamical friction leads to growth or decay of the eccentricity of the orbit of a massive body, depending on whether the distribution function of the stars is predominantly radial or tangential. The accelerated relaxation implies that there are regions in nuclear star clusters that are relaxed in angular momentum but not in energy; unfortunately, these regions are not well-resolved in nearby galaxies by the Hubble Space Telescope.Comment: 34 pages (LaTeX2e format), 2 PostScript figures, uses epsf.sty and aaspp4.sty (AASTeX v4.0), submitted to New Astronom

The shape of online meetings

Live videoconferencing has become an integral part of international virtual learning and working with professionals, educators and students using online meetings to enhance their collaboration from different parts of the world. This paper explores the visualization of a set of different online meetings produced by the FlashMeeting' videoconferencing system. Our polar area visualization analysis reveals interesting patterns in participant dominance in online meetings: seminars, interviews, moderated project meetings, peer-to-peer meetings, web-casts and video lectures. Visualizing patterns in the use of foreground and background communication channels is a promising way to help us to start to explore individual user roles in different communities and in different meeting types

A physiological measure of shifting connections in the Rana pipiens retinotectal system

The retinotectal connections of developing Rana tadpoles and froglets have been studied using light-pipe techniques to directly assay the pattern of the projection from the retina to the tectum. The projection site of the retina surrounding the optic nerve head was determined at two different stages of development (late larval and metamorphic frog) on the same animal. Small electrolytic marker lesions were used to mark the tectal sites to which the optic nerve head projected at these two times. Comparison of the positions of the two lesions gives a direct measure of the shift in the projection during the interlesion time interval of one week. The results indicate a shift in the projection of 275 µm week–1 in late larval life. Previous work in Xenopus using the light-pipe techniques indicated a qualitatively similar shift during equivalent stages of development, but significantly smaller in magnitude. In the present study, topographic postsynaptic units could be recorded at all stages investigated, indicating functional synapses between the optic nerve fibres and the tectum. Thus, these studies offer evidence of a significant shift in the functional connection pattern of the amphibian retinotectal map during development, in agreement with the recent anatomical data from other laboratories on the Rana and goldfish visual system

International real business cycles with endogenous markup variability

The aggregate impact of decisions made at the level of the individual firm has recently attracted a lot of attention in both the macro and trade literatures. We adapt the benchmark international real business cycle model to a game-theoretic environment to add a channel for the strategic interaction among domestic and foreign firms. We show how the sum of strategic pricing decisions made at the level of the individual firm can have significant effects on the volatility and cross country co-movement of GDP and its components. Specifically we show that the addition of this one channel for strategic interaction leads to a significant increase in the cross-country co-movement of production and investment, as well as a significant decrease in the volatility of investment and the trade balance over the benchmark IRBC model.Industrial organization (Economic theory) ; Business cycles - Econometric models ; International finance ; International trade - Econometric models ; Gross domestic product